The shape-preserving quadratic spline interpolations introduced by Schumaker need users to adjust the slopes to satisfy monotone condition

We study carefully the reasons of requiring users to adjust the slopes and introduce a new method that does not need the users to adjust the slopes. The new method first finds out the intervals that do not satisfy monotone conditions

then chooses additional split points that are given suitable slopes to satisfying monotone conditions

at last constructs shape preserving polynomial interpolation based on the method of Schumaker. Examples are given to illustrate the efficiency of the interpolation.